Premium
What is regularization, its role and place in solution of isothermal problems for heavily loaded elastohydrodynamically lubricated contacts?
Author(s) -
Kudish Ilya I.
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3891
Subject(s) - regularization (linguistics) , isothermal process , instability , mathematics , numerical analysis , mechanics , mathematical analysis , thermodynamics , computer science , physics , artificial intelligence
A typical defect of numerical solutions obtained for isothermal heavily loaded elastohydrodynamically lubricated (EHL) contacts such as solution instability is considered. A detailed analysis and numerical examples of solutions for dry and lubricated contacts with instability are presented. The main roots of numerical instability are discussed, and a regularization process, that is, the process that makes the numerical solution stable, is revealed and analyzed. A regularization of EHL problems slightly modifies the problem equations to make their numerical solution stable and convergent. The level of this problem modification is controlled by just one parameter. The effect of the level of regularization on parameters of EHL contacts is considered. The idea of such a regularization comes from the solution of a thermal EHL problem with low generation of energy in the contact. Some examples of regularized numerical solutions for classic EHL problem and an EHL problem that takes into account tangential surface displacements caused by frictional stresses are presented. The approach showed its effectiveness and application simplicity for very high values of pressure viscosity coefficients. Copyright © 2016 John Wiley & Sons, Ltd.